Place 1 cup of cubed butter butter in a small, light-bottomed pan and brown (see above blog post about tips and tricks to accomplish brown butter). Melt the butter on medium heat and use a heat-proof spatula to stir consistently. It will start to foam, but keep stirring. It will be done when there is no more white foam, the milk solids are brown, and it will have a nutty smell. When this happens immediately transfer it to a heat-proof container. Let cool slightly. Place in fridge and chill until mostly solid but still soft. If you poke it with your finger, you should be able to make an indentation.
Using your mixer, cream together the brown butter, confectioners sugar and granulated sugar using the paddle attachment on medium speed.
Beat in your eggs and vanilla. If it starts to look separated, don’t panic! Turn your mixer up to a higher speed and combine until it comes together. Turn back the speed to medium.
With the mixer on medium, add in the flour and salt. Mix until combined.
Take your dough out of your mixing bowl, and wrap the dough in plastic wrap. Place in fridge and chill for at least one hour. I let mine chill overnight.
Pre-heat your oven to 325° when your dough is chilled and you are ready to bake.
Roll out the chilled dough on a lightly floured surface so that your dough is around 1/4 inch thick. Cut into desired shapes with a cookie cutter. Place cookies on a parchment-lined cookie sheet about an inch apart. If you are making squirrel cookies like I did, you can press a nut into dough where his little paws would be.
Bake 10-12 minutes until the bottoms of your cookies are slightly brown.
Let cool.